Optical spectra, relaxation, and energy transfer of Eu3+ and Cr3+ in a europium phosphate glass

J. Phys. Chem. Solids, 197 I, Vol. 32, pp. 2275-2284.

Pergamon Press.

Printed in Great Britain

OPTICAL SPECTRA, RELAXATION, AND ENERGY T R A N S F E R O F Eu 3+ A N D Cr 3+ I N A E U R O P I U M PHOSPHATE GLASS M. J. WEBER* Raytheon Research Division, Waltham, Mass. 02154, U.S.A. and

E. J. SHARP and J. E. MILLER Night Vision Laboratory, Ft. Belvoir, Va. 22060, U.S.A.

(Received 11 February 1971) Abstract--Optical absorption and emission spectra and relaxation of Eu 3+ ions and of C r ~+ impurities in a Eu(PO3)3 glass are reported. Europium fluorescence occurs from the ~Do state with near-unity quantum efficiency at low emperatures. The Cr a+ fluorescence occurs in the form of a broadband emission in the near-infrared which is attributed to Stokes-shifted 4T2 ~ 4A._, transitions. The Eu :'§ emission overlaps the Cr a+ absorption bands and both radiative and nonradiative Eu '~§ --~ Cr a+ energy transfer were observed. To investigate the transfer processes, the Eu 3+ fluorescence decays were measured as a function of temperature and chromium concentration. The results indicate that nonradiative energy transfer involves a combination of energy migration through the Eu ~+ system and transfer to fast-relaxing Cr a§ ions which act as quenching centers. 1. INTRODUCTION

THE OPTICAL absorption and emission spectra of europium metaphosphate glass have been investigated and are found to be similar to those reported for Eu 3+ ions in other glasses [1-3]. In undoped Eu(PO3)3 glass, the Eu 3+ fluorescence occurs with near-unity radiative quantum efficiency at low temperatures. This is in contrast to the behavior of Eu a§ ions in many crystals where at high europium concentrations self-quenching of fluorescence due to multiple-ion interactions is frequently observed[4, 5]. Although the Eu3+-Eu 3+ coupling in Eu(PO:03 is insufficient for selfquenching, resonant energy transfer is still possible. While this does not result in net relaxation of the excited Eu a+ system, it can lead to energy migration and subsequent transfer to other quenching centers. Migration of excitation to energy sinks has been invoked previously to account for the relaxation of *Research supported in part by the Night Vision Laboratory, Ft. Belvoir, Va., U.S.A.

rare-earth ions present as impurities in other glasses [6, 7]. Here these processes are studied in a 100 per cent rare-earth glass. Investigation of the energy level scheme and decay properties of Cr 3§ ions in Eu(PO3)3 glass reveals that they are well suited to serve as fast-relaxing sinks for Eu 3+ excitation. Europium-to-chromium energy transfer in an europium aluminum borate (EuAI3B4012) doped with chromium impurities has been reported by Blasse and Bril and was attributed to long-range electric multipole coupling between Eu 3+ and Cr ~§ ions[8]. Such interactions are active in E u ( P O 3 ) 3 : C r 3+ glass. The observed characteristics of the Eu 3+ decay and its dependence on temperature and chromium concentration indicate, in addition, that energy migration through the Eu a+ system to Cr a+ impurities also pays an important role in the relaxation of Eu 3+ ions. Measurements and interpretation of the absorption and emission spectra of Eu 3+ and Cr a+ ions in Eu(PO3)3 glass are presented below together with studies of the fluorescence

2275

2276

M.J. WEBER, E. J. SHARP and J. E. MILLER

kinetics following pulsed selective excitation. Calculations of the radiative contribution to the excited state lifetimes are made to determine the quantum efficiencies in the absence of energy transfer. Pulsed and steady-state experiments are then employed to establish the existence and nature of radiative and nonradiative EuZ+-to-Cr 3+ energy transfer. The dependences of the energy transfer on chromium concentration and on temperature are also examined. A detailed elaboration of the theory and interpretation of the processes active in the nonradiative transfer is presented in a separate paper [9]. 2. EXPERIMENTAL PROCEDURES

Samples of chromium-doped Eu(PO3)3 glasses were prepared at the National Bureau of Standards. The starting materials consisted of reagent grade ammonia phosphate, europium oxide, and chromium oxide of 99.99 per cent purity. The batch ingredients were fired for 4 h r at 850~ in a Vycor crucible and were then transferred to a platinum crucible where they were melted at 1450~ for approximately 2hr. The charge was then poured on a heated plate, placed in an annealing furnace at 600~ and cooled over a period of about 8 hr. Undoped samples of Eu(POs)3 had a very pale peach coloration; the chromium-doped samples were green. The measured density of the europium metaphosphate glass was 3.48 gm/cmS; the refractive index at 643-8 nm was 1.585. A spectrochemical analysis of the impurities in the undoped Eu(POs)s glass is given in Table 1.

Table 1. Spectrochemical analysis of impurities in undoped Eu(POa)s glass Element Ca, V, Mn B, Mg, All, Si, Fe, CuJ Cr Rare earths (other than Eu)

Concentration (wt. %) 0-01-0.001 0.001-0.0001 0.0001 Not detected

Absorption spectra were recorded using a Cary 14 spectrophotometer. Fluorescence studies were performed using a 0.5 m grating monochromator equipped with a cooled S-1 photomultiplier detector; the excitation source was a high-pressure xenon arc lamp. For recording excitation spectra, another grating monochromator was introduced between the source and the sample. The sample was contained in a quartz dewar through which flowed dry nitrogen gas. By a combination of a liquid nitrogen heat exchanger and a nichrome wire heater, the gas temperature could be varied continuously from 77 to 700~ The sample temperature was measured with a thermocouple. Pulsed selective excitation and fluorescence decay studies were performed in the above optical arrangement by replacing the xenon arc lamp with a xenon flashlamp, the total flashlamp pulse duration of ~5/~sec. Fluorescence decay signals were displayed directly on an oscilloscope and photographed. 3. OPTICAL PROPERTIES OF EUROPIUM

Spectra The observed optical absorption and emission spectra of Eu(PO3)3 are characteristic of transitions between the lower energy levels of the 4 f 6 configuration of trivalent europium. The absorption spectrum recorded at room temperature is given in Fig. 1. The absorption bands at approximately 580-600, 525, 465, 415, and 390 nm are identified as transitions from 7Fo;and 7FI levels to the ~D6, 5DI, 5D2, 5D3, and other 5/9, ~G, SL states of Eu 3+, respectively. The wavelengths, intensities, and widths of these 4f-4ftransitions are in general similar to those observed for Eu 3+ ions in other glasses [1-3]. Fluorescence was observed from the 5Do level at 17,280 cm -1 to levels of the rF ground multiplet. N o fluorescence from ~D1 or higher excited states of Eu a+ was observed. This is not unexpected since at high europium concentrations these states are usually quenched by ion-ion interactions and 5D0 is the only

EUROPIUM PHOSPHATE GLASS

2277

Eu(P03)3 ciE

5D.SG,51.-

5Dz

~'D,

5D0

8 {IE

0.4

A

~o

--

~

6ho

7bo

sbo

9~o

,~

Wovelengfh(nm) Fig. 1. Absorption spectrum of Eu(PO3)= glass at 295~ crn, B = 0.465 cm.

metastable state. T h e SD0--* 7Fj spectra rec o r d e d at 77 and 600~ are shown in Fig. 2

(the transitions to 7F5 and 7F6 are very weak and are not included). The wavelengths and relative intensities of the various transitions are given in Table 2. The energy level scheme derived from the absorption and fluorescence spectra is illustrated in Fig. 3. Divalent europium, which may be formed by electron transfer, can give rise to strong emission in the near-ultraviolet [10]. A search was made for the characteristic fluorescence expected from Eu 2+ but none was found. T h e 5D0--> 7F1 fluorescence lines o f E u a+ are magnetic-dipole allowed transitions; the

Sample thickness: ,4 = 0.056

o t h e r fluorescence lines arise f r o m f o r c e d electric-dipole transitions. T h e large ratio o f the fluorescence intensities for the SD0 --> 7F2 and SD0 --> rFI transitions implies a low symm e t r y field at the e u r o p i u m site [2]. R o b i n s o n and F o u r n i e r [ 1 1], f r o m optical absorption and emission studies o f Y b a+, h a v e suggested that the Yb a+ ions are located at sites o f n e a r octahedral s y m m e t r y in rare-earth (RE) metap h o s p h a t e glasses having a p p r o x i m a t e compositions RE(POs)3. In the present glass, the splitting o f the SD0 --~ 7F1 transition into three resolvable Lines (complete r e m o v a l o f the J - d e g e n e r a c y ) indicates that the s y m m e t r y at the E u a+ site is not only non-cubic but l o w e r

Table 2. Wavelengths and relative intensities o f 5Do --* TF fluorescence transitions o f E u 3+ in Eu(POs)3 glass Terminal state

Relative intensity

Peak wavelengths (nm)

~F0 7F1 7Fz 7F3 TF4 7Fs rF6

0-8 13"8 67"7 3.4 12"8 0.4 1-I

578"7 588"0,592"3,596"8 611"4, 615"2,619"2,622.9 653"4, 661 "2 690.4, 710-9 ~- 746 ~ 810

2278

M . J . W E B E R , E. J. S H A R P and J. E. M I L L E R

Eu (PO~)3 600~

--II->, :,= o~

I

I

i

i

I

I

I

Ix-

uY 77"K

L L0

?o

575

It_--

LL~

P

6;0

600

6 7' 5

,

,

700

7 5

Wovelenglh~nm) Fig. 2.5D0 --* 7F fluorescence spectra of Eu(PO3)3 glass. T h e gain for 600~ spectrum was increased by ~ X5.

than axial symmetry. Also, unlike Yb a+ where the J-manifolds are well separated, significant J-mixing between the rFj states of Eu 3+ is probably present which can further reduce the selection rules for radiative and nonradiative transitions. The Eu 3+ absorption and emission lines in Figs. 1 and 2 are broad even at low temperatures as is typical for rare-earth ions in glasses. Although the structure observed in the optical spectra indicates distinct symmetry at the Eu ~+ site, the width and asymmetry of the lines indicate site-to-site variations in the crystal field. The width of the 7F0 ~ SDo transition, which is least sensitive, to local fields, is ~ 60 cm-'. This is much greater than would be e x p e c t e d i f the sites were all equivalent. The observed broadening can arise

from the existence of non-uniform, nonidentical ligand fields caused by a variety of local site symmetries and by different ranges of rare earth-oxygen bond distances. Recently a model for the rare-earth ion site in phosphate glasses has been proposed [12, 13]; it involves coordination by three PO4 tetrahedra and associated distortions which reproduce many of the features of the observed Yb 3+ lineshapes. A similar model may be apropos for the present glass. At elevated temperatures the spectra become broadening due to thermal vibrations. This thermal broadening eventually becomes comparable to the inhomogeneous broadening due to the unequivalent sites and accounts for the loss of structure in the spectra seen from Fig. 2.

EUROPIUM

5GSL 5D

PHOSPHATE

26,131cm -I 25,224 24,155

GLASS

degeneracies g~ and gj, Tji f

)

5D2

,o ll,ll 5DI

7F 5 4

2 I 0

2279

kij(p) d v

c2Ni gi 87rn2p~j '

-- gj

21,551

19,055

M7,280

~-.4935 crn =1 ~ 5875 2796,5055 1975, 2158 924,1025,1130,1228 275, 597, 524 0

Fig. 3. L o w e r energy levels o f Eu '~+ in Eu (POa)a glass; individual Stark levels are not shown. Energies are in cm-L

Fluorescence kinetics The Eu 3+ fluorescence kinetics were examined after exciting an undoped Eu(PO3)3 sample with radiation from a xenon flashlamp. The risetime of the europium 5D0 fluorescence following selective excitation at 466 or 395 nm was < 5 p , sec, thus indicating rapid decay from the higher excited Eu 3+ states to 5D0. The 5Do fluorescence exhibited a simple exponential decay with a characteristic lifetime of 2.1 msec at 77~ The observation that the decay can be fitted by a single exponential indicates that site-to-site variations are not so large as to cause greatly differing decay rates. The temperature dependence of the lifetime is shown in Fig. 4 and is discussed later. The radiative contribution to the 5D0 lifetime was found from the Einstein relationship between the integrated absorption coefficient k(u) and the spontaneous emission lifetime T[14]. F o r electric-dipole transitions of frequency vu between levels i and j having

(1)

where N~ is the number of Eu 3+ ions per cm 3 in level i, n is the refractive index, and c is the velocity of light. The three peaks in the 580620 nm region labeled 5Do in Fig. 1 correspond to transitions to 5D0 from the 7F0 ground state and thermally populated levels of the 7F, and 7 F 2 excited states. The integrated absorption coefficients of these lines together with the Boltzmann populations N~ for the initial level i were used in equation (1) to find the spontaneous emission probabilities T~]-I from ~D0 to 7F~ and 7F._,. The results were in good agreement with the corresponding relative fluorescence intensities in Table 2. The total radiative decay rate was determined by summing the probabilities from 5Do to all levels of 7 F , that is, __1= ~ 1 . ~'~ Zji

(2)

.

The r~ values were found from the above results and the relative fluorescence intensities in Table 2. Using equation (2), the total calculated radiative lifetime was 2.3 msec; the uncertainty was estimated to be + 10 per cent. This agrees, within the estimated error, with the measured ~Do lifetime in Fig. 4 extrapolated to low temperatures. Therefore the 5D0 decay in undoped Eu(POa)a has nearunity quantum efficiency at low temperatures. This result may seem surprising since quenching of europium fluorescence by multiple-ion interactions is frequently observed[4, 5] at Eu 3+ ion densities such as that present in Eu(PO:3)a glass. However, because of the site-to-site crystal field variations in glasses, and the large average separation between Eu 3+ ions, the probability for these processes is reduced and thereby the quenching. N o concentration quenching of Eu 3+ fluorescence in the borates Yl-xEu~AI3B4012 [8] and Gdl_~Eu~A13B4012 for 0 < x = 1 has

2280

M . J . WEBER, E. J. S H A R P and J. E. M I L L E R

also been reported[15]. The absence of quenching in these compounds, which have the huntite structure, is probably associated with the large distance between neighboring rare-earth ions (5-9 A) and the presence of intervening BOa groups which reduce possible exchange coupling.

io 4

Eu(P03)3

: Cr

Radiative lifetime 2

-

5

Undoped

4.

6

OPTICAL PROPERTIES OF CHROMIUM

Spectra

io 2

I 0

I 200

i

I 400

Temperoture

,

I 600

(~

Fig. 4. Temperature dependence of the Eu 5+ (SDo) fluorescence lifetime for an undoped (see text) and three chromium doped Eu(POz)3 samples.

The absorption spectra of trivalent chromium impurities in glasses have been studied extensively [ 16-18]. Tischer [ 18], in particular, has investigated and analyzed the spectral properties of Cr 3+ in several different phosphate glasses. Landry, Fournier and Young [ 17], from optical and spin resonance studies, have proposed a model in which Cr 3+ ions in phosphate glass are octahedrally coordinated by 0 2- ligands in a locally well-defined complex. The spectra, therefore, are attributed to ions residing in a crystal potential of predominantly cubic symmetry.

zE

,,z,/

; Absor0n

-8

Q

Emson

t~176 e

0

I

I

60O

~

I

Wavelength (nm)

Fig. 5. Absorption and Cr a§ emission spectra at 295~ of Eu(POs)3 glass containing 0.3 per cent Cr. Samplethickness: 0.22 cm.

EUROPIUM

PHOSPHATE

GLASS

2281

The absorption spectrum of Eu(POz)3 glass 77~ To account for this relaxation, we condoped with chromium is shown in Fig. 5. The sider the probability for radiative decay. broad Cr 3+ bands are evident from a com- Because of the large Stoke shift between the parison of Figs. 1 and 5. The peaks in the Cr 3+ 4/1., ~ 4T2 absorption and emission bands, a absorption spectrum, following Tischer's generalized Einstein relationship[22] must assignments[18], are: 2E(2G) - 14450 cm -1, be used in place of equation (1). This is ZTi (2G) -- 15020 cm -1, 4T2 (4F) -- 15630 cm -~, given by 2T2(2G) - - ~ 20600 cm-', 4T,(4F) -- 21800 f = [Ee,,( uij )12 N cz cm -~. Assuming simple octahedral coordinaLEest(vji) J 87rn(u~)n(u~) tion of the oxygen ligands, the spectrum can "rji ko(u ) du be interpreted using a crystal-field strength D q = 1560cm -1 and a Racah parameter x u,j gj 6r: l is the electric-dipole matrix element doped Eu(PO3)a in the form of a broad emisbetween component states y and 6 of levels i sion band centered at approximately 900 nm. andj. F o r broad bands, the frequencies vo and This fluorescence band is included in Fig. 5. The emission was similar to that observed by v~i are some suitably averaged absorption and us from Cr 3+ impurities, in an AIMg2(PO3)3 emission frequencies; here these are taken glass and attributed to Stokes-shifted 4T2--* simply to be the band peaks. In applying 4A 2 transitions [19]. The origin of the emission equation (3) to find the radiative lifetime ~"for band can be understood from the schematic the 4T., band, it is necessary to subtract from configuration coordinate diagram for CIa+ in- the broad absorption bands in the 600-800 eluded in Fig. 5. Depending upon the relative nm region of Fig. 5 contributions arising from location of the minima of the excited 2E and 4A 2 ~ 2E and 4A z ~ 2T, transitions. A de-. 4T bands and the distance of the minima from composition of these bands was attempted in the crossing point of the two potential energy Ref. [18] assuming Gaussian-shaped bands; curves, emission may arise from either the results indicated that about 80-90 per cent Z E --~ 4.,42 (R-line fluorescence) o r 4 T 2 ---) 414 2 of the absorption intensity in this spectral transitions. The latter, being spin-allowed, are region originated from 4A2---> 4T., transitions more probable and have been observed from and we shall assume this is also true in the several Cr-doped crystals [20] and chromium present glass. A large uncertainty exists in the complexes[21] where the 4 T 2 minima were choice of the electric-dipole matrix elements sufficiently low. The minimum of the 4T2 band because, depending upon the nature of the of Cr ~+ in Eu(PO3)3 glass appears to be located emitting center, they may differ significantly such that 4T.,--~ 4A2 emission predominates for transitions involving absorption or emission. Taking the matrix elements to be equal even at 77~ and using the integrated absorption coefficient at 295~ we find a , of 26/zsec. This is within Fluorescence kinetics a factor of two of the measured lifetime. In The decay of the Cr 3+ emission, when ex- view of the approximations made and the fact cited at wavelengths greater than 600 nm so that the radiative quantum efficiency is not that only Cr 3+ ions are excited, was only known, this result is consistent with the hypoapproximately exponential and fast: - 15-25 thesis that the Cr ~+ emission originates from /zsec at room temperature and 25-50/zsec at the 4 T 2 state.

2282

M . J . W E B E R , E. J. S H A R P and J. E. M I L L E R 5. ENERGY TRANSFER

Energy transfer from excited Eu 3+ ions in Eu(PO3)3 glass to Cr 3+ impurities is energetically possible. Comparing Figs. 2 and 5, one sees that lines in the 5D0--~ 7F fluorescence spectrum of Eu a+ occur in the region of the 4.42 --~ 2E, 2T1, 4T._, absorption bands of Cr a+. This spectral overlap is essential for either radiative or nonradiative energy transfer. In addition, at all temperatures investigated the Cr 3+ fluorescence lifetime was very much less than that of the 5D0 state of Eu 3+, hence Cr 3+ impurities can serve as fast relaxing energy sinks for excited Eu 3+ ions. Energy transfer from trivalent rare earths to Cr 3+ has been reported previously in other compounds/8, 23]. The existence of Eu 3+ ~ Cr 3+ energy transfer was established from the presence of Eu 3+ lines in the excitation spectrum of the Cr a+ emission. In Fig. 6 the excitation spectra of the Eu 3+ fluorescence and the Cr 3+ fluorescence are shown. Comparison of the two reveals that both Eu 3+ and Cr ~+ absorption

[ ~~,

D,G.L 5~s

t5 Dz

co ~~

Eu(P03)3:Cr3~

__,'r I.iJ t.) 40O

600

800

Wovelength(nm)

Fig. 6. Comparison of the excitation spectra of the 4T~ ~ 4A2 fluorescence of Cr a+ (bottom) and the SD0 ~ 7F fluorescence of Eu a§ (top) for Eu(POa)a : C r a+ (0" 1 per cent) at 77~

bands are present in the latter spectrum. The kinetics of the transfer were studied using pulsed selective excitation techniques. The decay of the broadband Cr ~+ emission was found to be dependent upon the excitation wavelength used. When excited at wavelengths greater than 600 nm, corresponding to the Cr 3+ absorption bands, the decay was fast, 15/~sec at room temperature. When excited via the Eu z+ absorption lines, however, the Cr 3+ fluorescence exhibited an additional longer decay component characteristic of the Eu 3+ 5D0 lifetime. This indicates that the Eu 3+ excitation first decays to the 5Do state before being transferred to C r a+. The appearance of Eu 3+ lines in the Cr 3§ excitation spectrum and the transient experiments above both demonstrate the existence of Eu 3+ ~ Cr 3+ energy transfer via the 5Do excited state but do not establish whether this transfer is radiative or nonradiative. Radiative transfer was evident from observed changes in the relative intensities of Eu 3+ emission lines for samples having different chromium doping levels. Note that Eu 3+ transitions from '~D0 to 7 F 4 o c c u r at wavelengths near the peak of the Cr a+ absorption and thus would be more strongly absorbed than, for example, transitions to 7F2 or 7F,. The ratio of the 5D0 ~ 7F,_, to 5D0---~ 7F4 fluorescence intensities was measured and found to increase with increasing Cr 3+ content, thereby confirming the presence of radiative energy transfer. Energy transfer may also occur nonradiatively by direct interaction of an excited Eu 3+ ion with a nearby Cr 3+ ion and/or by energy migration through the Eu 3+ system to Cr ~+ quenching centers. The importance of these processes is dependent upon the Cr 3+ concentration and, in contrast to radiative transfer, will be reflected by a change in the Eu 3+ decay time. The decay of the 5D0 fluorescence of Eu a+ was therefore measured for an undoped and three different chromium-doped Eu(PO3)3 samples/24] and for temperature ranges from 77 to 650~ The transient decays of the undoped sample were exponential. The

EUROPIUM

initial portion of the decays of the Cr3+-doped samples, on the other hand, were nonexponential; the final portion of these decays, however, could be fitted by an exponential law. The characteristic time for this latter decay is plotted in Fig. 4 and is seen to decrease with both increasing Cr content and temperature. The complex decay behavior observed for the chromium-doped samples and its dependence on concentration and temperature are consistent with a model of diffusion-limited relaxation [9]. The relaxation, in such cases, is composed of an initial norlexponential portion arising from donors which interact directly with acceptors via multipolar or exchange forces and a final exponential portion arising from more distant donors which relax by diffusion and by intrinsic processes. As the concentration of quenching centers is increased, the average distance the donor excitation must migrate to reach a center is reduced. This accounts for the shorter lifetimes at higher Cr a+ concentrations in Fig. 4. The temperature dependence of the relaxation time can arise from changes in the diffusion coefficient or from the increased probability of additional relaxation processes. As shown elsewhere, the predicted temperature dependence of the diffusion coefficient agrees with the observed lifetime behavior[9]. Thus the model for the nonradiative Eu3+-to-Cr 3+ energy transfer in Eu(PO3)3: Cr is one involving a combination of energy migration through the Eu 3+ system and transfer to fastrelaxing Cr 3§ ions which act as quenching centers.

Further experiments T w o series of additional measurements were made to study the process of energy transfer to Cr a+ impurities. In the first series, the room temperature excitation spectrum of the Cr 3§ emission was recorded for samples containing 0-05, 0-1, 0.3 per cent Cr. It was found that the intensities of the Cr 3+ excitation bands increased relative to those of the

J,P.C.S. Vol. 32. No. I0-- B

PHOSPHATE

GLASS

2283

Eu 3+ excitation bands with increasing Cr content. In the second series, the excitation spectrum of a 0-1 per cent Cr-doped sample was recorded at 77, 295, and 400~ In the latter experiment, it was found that the Eu 3+ band intensities increased relative to the Cr ~+ bands with increasing temperature. The above results, together with the Eu 3§ lifetime data in Fig. 4, are consistent with the hypothesis that the dominant Eu z§ relaxation in the samples studied occurs via Cr 3§ impurities which act as quenching centers. To see this, consider a simplified model in which excited Eu 3+ ions in the ~D0 state decay at an intrinsic rate l/r0, due to radiative and nonradiative processes, and at an effective transfer rate 1/rr due to energy migration and transfer to Cr 3§ impurities. Since both excited Eu 3+ ions and excited Cr 3+ ions decay rapidly to their metastable 5D0 and 4T2 levels, we can, for the present purposes, treat both ions as essentially two-level systems; that is, the effective transitions for Eu a+ are ~D0 ~ 7F, and for C ~ +, 4T2 ~ 4Az. The rate equations for the excited state populations n~r and n*u are

dn~r -d-[ -

1 , 1 , (rc---~r+Pcr)ncr+ Pcrncr+ rr nEu'

(4)

and 1 1 , dn~u =--(~+~-Tr+ Pv'u)nEu +

(5)

where Pcr and PEu are the optical pumping rates per ion. The intensity I of the Cr s+ fluorescence is proportional to the excited Cr s+ ion population. In a steady-state experiment, we have, from equations (4) and (5), __ " r c r P c r N c r

"rcr'rEuPEuNEu

n~r -- 1 +~'crPcr brr(1 +~-crPcr) (1 +~'EuPEu)" F o r the usual (i.e., r P ~ 1),

limit

of

weak

pumping

n~r -- "rcrPcrNc~ + rc~%u PE~NE./rT.

(7)

2284

M . J . WEBER, E. J. SHARP and J. E. MILLER

In equation (7), 1/~'Eu= 1/~'0+l/'rr and N c r and N~u are the total numbers of Cr 3+ and Eu a+ ions, respectively. We now examine two regions of the Cr 3+ excitation spectrum: one at a frequency Vl where only Eu a+ ions are initially excited and therefore Pcr(Vl) = 0, and a second at a frequency v2 where only Cr a+ ions are excited. The ratio of the Cr a+ fluorescence intensities for the two excitation bands is, from equation (7), l ( u l ) __ I(V2)

PEu(I~I) NEu 7"Eu Pc~(V2) Nc~ ~'r"

(8)

The appearance of Eu a+ bands in the Cr 3+ excitation spectrum requires, as expected, a finite transfer time ~'r. A t the other extreme, if the Eu 3+ ---> Cr a+ energy transfer is the predominant cause of Eu a+ relaxation, zEu will be approximately equal to ~'r and the relaxation times drop out of equation (8). In this case the Cr a+ bands should increase relative to the Eu a+ bands in proportion to Ncr, which is in qualitative agreement with the above observations. The explicit change in the ratio in equation (8) with temperature is more difficult to predict because the P's and z's may both vary with temperature. At high temperatures and high Cr concentrations, where ~'E, ~ rr, the largest change with temperature is probably the increase in the total pumping probability PE,, as the rF1 and rF2 levels, with their larger absorption cross sections, become populated. Thus the simple model used here would also account qualitatively for the observed variations in the excitation spectrum with temperature. Acknowledgements-The glass samples used in these experiments were prepared at the National Bureau of Standards by G. Cleek and D. Blackburn; we are very

grateful to them for preparing the glasses and for measuring the density and refractive index. The experimental assistance of T. Varitimos throughout all phases of the spectroscopic measurements was especially appreciated.

REFERENCES 1. K U R K J I A N C. R., G A L L A G H E R P. K., SINCLA I R W. R. and SIGETY E. A., Phys. Chem. Glasses 4, 239 (1963). 2. G A L L A G H E R P. K., KURKJIAN C. R. and B R I D E N B A U G H P. M., Phys. Chem. Glasses 6, 95 (1965). 3. MACKAY J. H. and N A H U M J., Phys. Chem. Glasses 9, 52 (1968). 4. VAN U I T E R T L. G. and IIDA S., J. chem. Phys. 37, 986 (1962). 5. VAN U I T E R T L. G. and J O H N S O N L. F., J. chem. Phys. 44, 3514 (1966). 6. PEARSON A. D. and PETERSON G. E., Appl. Phys. Lett. 8, 210 (1966). 7. PEARSON A. D., PETERSON G. E. and NORTHOVER W. R., J. appl. Phys.37, 729 (1966). 8. BLASSE G. and BRIL A., Phys. Status Solidi 20, 551 (1967). 9. WEBER M. J. Phys. Rev. B (in press). I0. R I N D O N E G. E. in Luminescence of Inorganic Solids (Edited by P. Goldberg), p. 419, Academic Press, New York (1966). I 1. ROBINSON C. C. and F O U R N I E R J. T., Chem. Phys. Left. 3, 517 (1969). 12. ROBINSON C. C. and F O U R N I E R J. T.,J. chem. Phys. Solids 31, 895 (1970). 13. F O U R N I E R J. T. and BARTRAN I~. H. J. chem. Phys. Solids 31, 2615 (1970). 14. RI N CK B., Z. Naturforsch. 3, 406 (1948). 15. BLASSE G.,J. chem. Phys. 46, 2583 (1'967). 16. BATES T. and D O U G L A S R. W., J. Soc. Glass Technol. 43, 289 (1959). 17. L A N D R Y R. J., F O U R N I E R J. T. and Y O U N G C. G.,J. chem. Phys. 46, 1285 (1967). 18. T I S C H E R R. E., J. chem. Phys. 48, 4291 (1968). 19. SHARP E. J., MILLER J. E. and WEBER M. J., Phys. Lett. 30A, 142 (1969). 20. GLASS A. M., J. chem. Phys. 50, 1501 (1969) and references cited therein. 21. S C H L A F E R H. L., G A U S M A N N H. and WlTZKE H., J. chem. Phys. 46, 1423 (1967). 22. FOWLER W. B. and D E X T E R D. L., Phys. Rev. 128, 2154 (1962); J. chem. Phys. 43, 1768 (1965). 23. BLASSE G. and BRIL A., Phys. Lett. 25A, 29 (1967). 24.. Nominal mole per cent Cr values are given. 25. The signal-to-noise ratio decreased rapidly at higher temperatures, thus making additional measurements impractical.